# golden precision oracle table
# generated by scripts/gen_golden_precision.py
# each line: <input_raw>\t<expected_raw>
# input_raw is the storage integer of x at the tier scale.
# expected_raw is the half-to-even rounding of f(x) at the tier scale,
# computed by mpmath at max(700, 2*SCALE + 64)-digit precision.
702243952296358473738026482186442972199339635014092690167340436070396197380318487393771485836611875257158806299027551585015952103756026078385224304349973665	837999971537206243202504797252966874216541787864204774214361313597152967215978124673762363608923567721741286446590424693359603073650308127772768058970194
8836027642561895695795712935329353445980704716499200030882939989933335350629726355242757593566089266171545395644229656713391431485101450357765816843338371	94000147034788704610139912690124747525048043433053844953866948500978334876412906189326146052313326744491762712484262273360357428925728433066935733431536
461040948168891914915090652985422706862841467519532518347584715209160593093291726164257511109095696200196843126550286252841234731823218617139870612725806939	678999961832761751234915401317364423185750384917101017469909673149067473655191628813387352006294308561779457479879155661486020165758799449939378882628888
94248924052589921289505497380252302441919656942650606905489910819410666561550786319309916925475396887572370180722010605851464638185941790770032890392813652	306999876307124790492064987748492592457227872340839403533619452128422009621566962520388369922471787493893741520025122649247249636315516968920115189528312
609961033399725919039592306859157234045106174794865881810742265067477117047836276005472422053476921959672191463598058958388787290464139917908446925205342841	781000021382666748925195269697808880691843767264078524956415370987507050563690234544784264404473267329194984519728920683155052507957334039407134028351607
579120989908714654013766115739709114791377043809931750933548205555024412128073913407560068163149765956598680244743953110627283470521271066554714436986147758	760999993369720505948199702034107865976350011612854194548331739811198045974048641659545369672451592983262916163529755849054384139367152001466663853227796
801024928440043304886312938781709050563315474602004853211478683250030906184213614577584378653026058050584451746508121447827799387050339994907650222670005910	894999960022369668533735206374422557262140867292959016035835478919686673720323032168004471575784270144542360018099497275582534562215165589960060534608361
483025005520026649762917040172117208096560834679751447827078770961785539061343401794836055155757684478852327480350880166778514595397331282270655132711184538	695000003971242182728167313879524157339807480752182188972406007504768147422217879770596458145330155895089030561897392668803486279583125092755504930616025
328328938945908051109326998750895147240194889881645564803072694858254666605983704816452391450006987854814204355017027167782270095646808639819924770617685298	572999946724175578355898074084456960921890357177409947623971535911619240388856417175843729776133291058902627044940016631878266937633980434154485581438749
126735984504315334650209355416601949343261161352487968481435912497147961025803914604911410562278032687113260522577071848952134660698636550903814386883475589	355999978236397276679502607996111507837205834025409075142138835358474056897568286250770756355732902281726600590237298634698323733841203353017425647662140
255024900730932275789641621799304354388977307346500274295841362895798964430841810333027949078801957009594473887221141963784523816727867523957291410906421518	504999901713784767930234630749051816343380695734534343489299387006168853192838474418042229671182739420272250490485324004658073924055522659765454081748619
9800904810240257784759878294436227757998774318504098034664278569091687380264182884641014883501406896288455926563716781813842968516658080219533726762189747	98999519242470353446707180435215665557570017831985044529790723074641365235016167632922473264977109607852188811457850168137664564209178655245163800878602
602176001024132961436774893494040985749426800623694556814362676630514570173824259852932487534865072316639250237068568742772846398925316832989119256487304569	776000000659879485181271880496740058261743916440471009366970490907323664066108499131250638069645185406733444007906426167061917494050659132896205606639526
54289095048580003453689510018461053206936901045034080616917755865476194204167830846011813684544135725283871514867073736359164913249503495462222420287442021	233000203966820602982366139112923872085098702232524102389073838240402052103620183936430247937272310154138778168734605587053049941371143127012366635851550
488601009008793797661207749292124090632131016900582746158132343122731533800597147287764275784748047428767325728247586107527946924724598006836106136907577971	699000006444058480783489302957447722885418722044985891803966641573186327373452439158419969297218860241134208607569863732464849778584180856676994301829783
262143976835700147802022667801430988525385586242907219585215065483062582048479571647252408375737173679381613169244206271724176581791293259332184197397142077	511999977378612925854364755349811553522436339975769684859843599436396744194306743842229191000120638205635222297473050470823967809820903999510410702388252
269360974357403193080160193629263503683410207163589370302165753477821156531417401221907838391355679752703212269432407842155382967663153658016004836865412886	518999975296148923699327739486878838913454127234150284801011228767813687944494306520708266646671591496387363959604039129886363207689005543854652403933862
561001047410191226265560427499977351197958375450273120869083989905886092409243139785469054390648006379123200417986726366383483957650153160056085190297490216	749000031648992139256913883013385248565262286331217264593816211198642150009673667226241982183046423934529542962694384084182820274484003663329042536572529
39204031903697938629614085004026128834006648302294668837445488346471329610118060843246176451413422449826025444887608198328120150377103340461667527369264825	198000080564877393762991446820517548602269546685603307789683281679840337934841199362661984967617844665192419735250080384419096034771881889468326008897135
868624071089658341203495536610986858548965120421684898595870395943631793705149732438245565386364912527428617503582989707097331054001851860532179305344604178	932000038138227943497352396163464325934937452972726929397646166348834681745192588406035863035161655076508049859716538401854235408864090600698119489878868
334083933276020579508214309889172149392447370170665490954167022374302748029469983153375836033242999995677800026441493719095130774656582079148090159077745016	577999942280291736975339395512014867751192543764423573835868125527480090725822425769523263091095894300989954672626548897897525744973102407055639729605294
368448907574501612693389337484739818134675585378694319543758674751436745382093598985013449447752527256837783238267795157625787638872316662104808425620727675	606999923866965252433615702911264471161563834176137534329961227958681494841446111574195870135233468883653112395205809039855435404478396243126168104023915
984738782322958526925113926371302165372772246958568503133990228286873395196534486741322104682912107456628631175470915464113121456935254113695671046141262060472027362670471440341581055847907160554567504889319946963593832241425105754255889469711864198370677700380325237829232039108133060389985083558298189878	992340053773381923206013295539865868436307685765002122180843006709332488114391785952302597715439791092885228599799703244509886290353970434392572904798299806281514622328980252399497876716610893281929392251495500653339071316180337
258756482555748025225485534762516595501655383674010951335419373724457720895921866844416218283606507374520143293204487326726338294446601116512457179367931688967828708277869527403092808870797726590276838691145566465681706503934865577920673257650039774039322708967966332552696086473766323711243223954767416481	508681120699154732474313372217635966126487227861036750853833461794809130227941096293586591741309089501310946305627018602418945237773585421912172936710998145833940266007825795692517162620253294142795100109084549539490741522976038
519155472885076053581537994248455094329989527362871572270105374082990489476327415633679004855912728304332298941643222278297558475311874030496791237733025325163537974649027083461913416044060861976775889752927712796733385373372335311615699882347933544708804373337324390438641839094882873673283034181060120133	720524442947687968011656646572436707790407083181610898576435481734065123800104060317776539723078433836075804837159188595050889977883595716902546888648618132996307431483120311128232754501342082127475499470452035706902189057991759
82277540210794154711692410954513379420827484642870577572354907266941413760523731569580990127145396516104626685696049391808442620524509312128200998583185462947859385547568474491470797431762731594826281095192654780684837153652647281825260676508277974455279938746927285737850683919952621595482398133244401963	286840618132777971308900229202557092133142691163914546209549333049666966624938936796169818773029434783676794366923912536001252840431650433278884554748187739544855715549841337019787115791686395689766247983909100287303818897923659
762968651233512923246058257882130357248999667556562544741781345797055579569122707032017186049581172546091264166522158840919403189268587231378604488905118152886226199099124661778436106496586826868198325559325786456886722096172310343285382911297627189866991386048636707494774791973249008260595755997248061447	873480767523540224653832527403287933591728235206677554988973881380324235341320060265835089169177858639623295327330593768845230727968385811678343445508015816460587064968581509279585767245969213448548739634900053842485005739029484
200490609145870108751179114041606071022008057851020384004881906456990886747708977096359318100005138495611963017875548480475484962053116034058716607360332833709257650321330959470594712612345619278107383029836629841695019099574191096261660004668236885454555610588033247713817307907223936276273428567591382869	447761777227433861219749617900370426068107913353546386144218510732716767248522105140447086765844538340561414011546618155143808154765338623517952522752960248257714703041763882532165331187925112245850731593020626108005636854471869
40557243397034283457558970460531345513132564868821054623828328100701603196273464508704380492285410409578073811717890149622535032121279574136231295508009838240007616849927223209591367939644033502722588782356114834275579218461719857992880523259628009283926600772372589449924278738666575939994581516611078245	201388290118949774694968415394330020711641458356354456422270982168838452249214345007670003248641252808732120798364817273773191608370468410264208983405424481952128484810605811441962128338365997306148949503536443429842694407412167
36660693440774245145551786141606342848862044635187410450711488549905683735747620800789576681852213887441307378008973907353584125000163341174297524217433079187585128457227175395967053011009465661412795237203196270761266994930835529619791229243906420941726530883082028613866392044228341829270184423715733940	191469823838573176730692474211461376755291689364243074009886533627073279737553762040825328064406489184053160999820884259916140670125052857763355753076425300866915249452795441312559786066062754339555462732265496353544745668614887
646206868362995609217614474175787415194049024663653060400578801440012695037945813344728753949994914275305575673341266170248458295009890027090553036153615001733739185047040246727606355698564838248460927564230326391887583577303772296254746016351623882556983599647090894027857692487468311715903483409026900825	803869932490944463498473039004016317056354312558623147027702822376393364373313596646040795005004817342252109409428905077407745416650134079104124465263777193232683927364796680331467079900467596413478124042458053098494351696687734
338176039114367960590758367625167542721029871357933230386321818214588971302229418774617724820111294322915745900052601202543643271707542595261038868186382556289737714918949616966153555424262649402142657765695858098630577115617186451591586921371984764870818981718761215619447751304147129964054806580499398550	581529052682983294981015141443047973659398126439234093145323760829111617502318088546969840216708442520084672518815772297229833433965238229287211332395348682893405052503587086221212223699968029390036174242784577130439499504544599
295262181018293324507822186371373745387842092699272596465883970228086206739291469812699829646553749121406563279263121508031930486070705213066216047230158346969355018216596192813324196004861691358342213221932304496409739516607405667172778387468469134210676288650403485684944552820880291064063381356670677629	543380328148059961130853116089716087256636830205880575390672545808319978305630719420901360239875589890352796548204100707029783015078166524124720547711601781806466113989275004482693397639580259327323361144660667729279579828654779
782935154142177310247647837247891063673926241783073886256892131223599618268170774390362909503966677551059845586063413773089340909547983193066750025694550367035933187568025366392535246518038986316333536448113636835828555595439099140820139150729673923733113003060845499898875012951069418079655540669152703772	884836230125200801413823548213677565556197451363504918163533419023169297001994873949554351993463833361125648418882660988257893025417168172286278432572270268820915035537304101298036476646485405387790665095652905511679377382112638
769192715499980412159575573543210725269165610378845285636202731159996555256139272886105497258562721806180530919563127017829874249029668232050737576065960264617903315011994753653341534404077463880634425548420028790516401213797505321315469845616076750742952087075890328738453697934093221760049369935569883543	877036325074383912863610641811392193224048065929556204272875933887471399408856710426175957678472500882483368849908936545495630349839877605470300424710416474758967616737938642564153619836551791385217991159015014293798848203572607
931901333768523473391000322412714423010092326767107826589456786698355980332839246374998426085604707931534504816715979261021183069001325120223513305047103933031063916401394193409452065296433768125917961210944715242084816352712683943847521796999231894513274211846822666768368572096458093819189491458356179383	965350368399227096597335138611132979440850471423619689365107675071819689016699158734756919108525996819429205934632723678867943853363899919599630500998212321748337288242911842755067296032228542547304265891063808868440339562013960
262874582879212911125208124498742577400957458344142284981358685414374082620492041012605944713147589274566312431159225394749486548196643170052984317942549470344208551350501333559181373440781277842928906859163168106402558962833882487836532717822910127513438911240974541004024631337024809779808462729743878840	512712963439791437389297699595902375104618048944799980168819945938109132726083298381132993793197162824768184895250365777165386233478552092090420170877318313400998307238410172489940519811201111491778180396557640551017862723838299
235780348391208311346554385939642531012740958764737600251981777535074215642225188138894970204001412565725561706939781036360414519484885005658453419505464157799754494955429605937134948254463504726268260522895100610120273070885468141502583794160814981128571303296013558348092679234498446138729923197773671691	485572186591456565632790916188830698704619813529505861698684537170227097263071765631349880735749260263288073906487531934466791640299275511642527774479563006542675779808584770119698408072460472694080559655248897293991166076050350
886923399145246436705260604156863034535423633690272174493950019664497228684851532984258935818221810398950697693957866981233115911712864470823094624707197702423375882716830959953421740457392813903867824428471984268582573127934150919031838794549702200011913493362705172377760008278606216013169956807353612156	941766106390141031765402363869894006468686642235042591817845179504913518035031081227994204694915229873549631513718647642080778347451601483575953589115455991054687044402544122914420458928508165697913185733670527545963713050150980
151749873561852954477471704434988266428191700807280074185196681507835134878694490248074890077080191630034650499016667032916401880779429135467369169696553554627448742817134858418660965398361111768977729071194129458840872031839106417797741070784994656789460452701975829164857965409305791024176084292529229973	389550861328598469417187028540119524372276413032583620555190104619930731364773917713033089260125527824785116698379555460873727705459089297871979265825840124591075575952637831066005072157993878924381816341534093428428818623968279
258048686667421038523487011909407530658927666830687200238648090457195652610332530224827522282858194051825424012780912001771582094401125960344506446588202126755074307179610878242266369028983424590649045515930850762634113082205849492508493394570340896691197477874554485323765002917280447612346911324247968670	507984927598665114688616629331870932050523512777057309293308731879299766619982751498945136145233771054370939780957773204369083209743028396643148132789814210116162547691943433588141147434787771819340532465571790254942194115443683
194373582150034377393048432290490010337666026371379475415257330807310095903998806880786952563839671561370150855718090183804369869282935991351617099508644613838028892373316294777759601128345030728840882048924924058169025030200311860469201299489348722819137637657333888341349942499802471485946276076064710702	440878194232867880667762151153017671050061249501198489742105464990969466472914228792692123905682299220500728875343962148242986552568635784971290093811403289864722733215433081505963788150336272978670002816044966098382845686586163
828223345051698042890653373932677056850172335077485829106593708328949095224971713907817563236915028564643596799405915421353464674888226865421180035372093650064112628458607994555352025257041143162445773531005299009758272673735842591579674812538818259286668909374949608524636827268616923728276206812248459382	910067769482964407487657523575462957762950124038968196993390552074012689350672902007649028617285018686077579540335538460329555076673594103383958039282920156266393463718078038405198208161571782382177594299281429970837846416941298
356162922347541815799550619608512761603173926604624776937794851310153673670901293277051173039411482118837106863087446430257792731312197437438756935731755743627305229874369553714138289836199402122542430288643677219345459457945213989449911731301802654866488059460305708238687300395679338723012508373083323435	596793869227509588195677331001155174108247605310115688364190499844374933142845354680894659065177191906894622961792691413844768296952351281682453360180452133884980738035712220235204880104394715529637900356653422465567776592437859
304539198444815170496849714475063529477364042876104605336488281881359071388311711376314806920516912246252468787786498248116096630258457445795123258972260664327445251277607616774557675479347191483887077054447522663534052701890064144483805617652215719926722555309867839691555466446952093257453152959244976291	551850703039160013079947284085132249168119235570884276126965644310853065850475713056227326864722701900075566885341892695540187289928586223537056864394232569901082083045956030611356359913251706345890720224890735554282995503202290
143980170196097026504037847962569529262973168859823469222491432536752721377038790662274197405513874206505334192675887434475720736270316753642162595385446495173308310155553872239380310824011214793601209111901617304582854371572122372382825916821993867525528858965242380213756518958280789534041253200436542547	379447190259852927671587585011598320714528126227793303432647579735157214080576928252742606231692781580935038113537471998911926542584148796179789570849247725982417930410379999282552882741325671585712876530756076609202804242259374
714208363969204996875210050343425866550317695467165511235354553399947452406562420642367229481887883600136657305295252771989144752925694538945857851814021716407562308288799352116526317305410866086447034806075655504192820148355816465767853667070033748746181720447052421603439926057214241374966791522321978544	845108492425206313448338678714341344144531917862637574327962207134311525968779552056818266259493160853380217527356966551607371249004271777166101692357107889067881884985309591570776482393344178453392220496196242825796400015900989
86743068466615478549609347332130101110272323263226733767698492079147378756022885681368192096937746562010594100772824138657762596458158873500296614326820211094405537705582876521923630967911173959445548324954059653292523065142296905777964709186206699561505633390467909417675970264855644283492524403678120189	294521762297144145262370636415697661043697817262463829538268544014870396149539607895356585425622898674705993883327623771671119579761365142347230322734521446259916682303605547958283244249785254152532891209608835285081554884876285
323609310619154469624339567912100806697616656796812172803263752545156663553334422426839444180415783068831750185676291178434389798286692506604695333954907209153051063787736116739718970124198282548675022574398756665447937812489581115504244328490216018915783139486367874104776590079103953655769053645183508250	568866689672681106989408986304350215988467029761421423184860308450402865448685102895288526956770240225379077603495792572367047727057340037483699821889999343594693710828732166492873519407706599081097169929541213449227119445230412
875550592086915115338423334840268197174222830416840888597642260783303915013693869052518192870860673580284138983462213189008278207024491021433539546911352317272641676044762008241553198886623523317004152876616056628819182065384146930012459346551608131282344297594529164400999153838722713823885044961641715516	935708604260383573041625964214359427643501725334122212457003099365442509719064592777000925863894569309071302758144653143177249479935141688138651210047857366085707025347667394623781660769030987466816328739226887545197230287470046
381217763682733860834252217377183421219646245082083881257464598103826815175542031839561143335532039263896045744125137813757142546139164714447592071300967855862734082840363691060993858660088861983584753494261192274453625931951907014992947275956507229385419982282087866458482795597100913859280807528567575511	617428347002900297541929837610251232084664310492443019568891635168597730045882200472151996081822642977558757624167832378273205881854487544759360920072415476710816945804624121577686104024365276312820343187007182993428473550017639
461747315738211837520121286562609894727945064090504853553989381657269371279552954466167072901109938344243281285388397154219652342269983151805909078654021734976324700328380183333114601986483393594492320215426761942049019941400291397374459065876968635769970262240137936998521434000202392860146748824468426309	679519915630301329816685004878722623723331169614344951767149774254866057267461853936998109572013310219948240791996935006923843357353482931980161808933177285720277875839488571687932888470339536428982797110670407821856781723629217
678685183856638315228760321849637937129157203082124883607325564643355205287706316051832152847467129458492577284639979299156526863313734412242301867108595366704361138663241705765903327410590038730308576898355687069147197440099648600767067382287339601865228438683478618349310482940605673007912192857836919170	823823514993738398101395002175497092611941557961077416217104905462972494213480859775056800385927545978980398366795796360276071969969616261069271556805364200758031398089404104325441166234954487109425851694172728331738673641671151
571961744723355020475583853467583156446836882364476548085632815092614956430126883559978848495698094317746073461118149241312081579710969504176033416869458716741962320633923233258221592747122766562501294798419712512432514375053647843995796181546291178317383968851000816062334880617452845219709466040004252966	756281524779863322343570204639054404606035859616718848931190937484536266815523247857722081998172130534105187192006887179605523737890514390591085404783705397481094870016187794409498751926234270678550851097707204652520779384209034
652903081055966225537198675288207290826641671096965915259979734189207302915681975975256672696359932744346221338816463817868285889298582068782410790231955067256762404978772112297384092056855575153776505048597016373934880381593363187657597721897052837214506656300692768272066394090426533509465657798776225003	808024183459855504303471812334363579507447841736303411130455066088742430357658271772156186214582820850180031442695088852915115538713530076208142157232312634722430830515786082819260691976566832968471261372202811053510906274651298
602321068985392268741332327904320333290677606913366448735271491738799988326081869258867754981392491712985140636283268548106870901926164969569151375767779332302219165463206841167889749028855881617775501279636172811490904295758579335647054852521672957089489753404936209292316329638145467681250064241138810365	776093466655526142718239174118537843152275276126125037530254035063014799580837239339293012150115287889753025038306172962230900758337818620023163092265046931770664759548644443510126370210114398651799769354246229028573704519705401
676384910565661892813094063898899565677748150468336953170381217471748512867545041024483648056752866866126761758959472393703453366830408990088617743895741578596476842882923675582731214944043333563531083071605697335972083683941302468533229886813894685635609635245459556347812521803584584711601779097649860162	822426234118089093446372863336891915911309790348178316278417002032848847538499926876497946959576877996430473541997298432793040856721201906391949562749378322016167487338785168559263145228181994170940797430233985254875649728368684
118100539677347604640095560054320076881567634147106957664184928424734425221678862892463040752900153176311642536656389221447833818045802938167301302189807062572084520981232342260847818870790029653941286584604988101898787950232379196706077790042417913428588731358258661163138657897858836756841601938074622379	343657590746003462463282702481725534993669556447417128334114008593409402565164986751376227951077838458588693541417166696799018528505185345870825661564177895659209390906347824918414810998434720421621994848613148469603914287915875
716221754207339447187874489133709390012387682738044566503599470629088679456001332599546939137998585856679837652032443373002067018391784385246181362290908217465518506358311648289503114479691088294613872993989177266166617895968723758761184694727469676757189871693065967770673198388565334961749603169657424808	846298856319290701656063645305038641197126871034830265748337109293565055994469616296825581843362076194837569728927311194207177642954361411352170373161016679783456662844158461955451832896499436614533589936580035756774754060246739
293677124383596972931782575347654465652960855238726234694529666234851376389818734669436209371400732620805393040138983880440265709664206811875992086379746317020356965973506211929256659251302804073925306114206295626131245470733990580202167376887096436634194308191007916063868910440416494723007110786486255551	541919850516288961056905632851828037420558663248264923072530389389622860868804648831519076528588281578190649827502191323230433582370128662422675332297316087600128334685193441624587918905869341604186811180341895015914154740483079
197294239132402040982346945434134613268502205073831188328353661406002519773702335756090031046629829912058868533648391120751029929013343302061988827693746447240985184215463305270159928249481210383892396252764463746201368362275890218363562704024639579519491922545811199032012982957532014394418960128131007653	444178161476227960873963223414716202696266089964755653077549681013698050485545624919248418832767592566938354026322584479385185744870493420255291619959531399038352882158159562585130968663809551619040985504488893784155580631272860
634868121151785564856200355036953356412519018624118339984956323518187503880003128452996745566895557819859612505558684791680594399247882485593797956567441542115810105548013523402954606795525907516869264605517383097705827880335026805169131364731918685090383351331791178328416482708590157257294839212651699154	796786120079777472058521746079678909624184238988021119682672394867384207436027065111383309112765195428578160564372803759930470622481199776299936189289923501235200621123952966610423734934834784744767803648865337405526927549836813
669177729075020570847443667595745956901296120166692251865309552261831016740149913695087654845689564577170717847931488572098582974465572628821542040276087490781935996630147424176605649559035591165328061283268745613358922755503695786353220390868946624854019352528542935142690829533316563500453555904202649826	818032841073645753448436412221473436662956222521353861395967511180583629062090032860036002954202474653704494790760526453689180081842714826271968468746399120640990532392451089250757337111250444393531334986276634635982040662565577
380800234111116945299008029005878669090244529375371354185561016429048961331305941539603378993203145438545627954416171786761695302547178892618890139405817573830146030704591246073797221592889268772945536797935782891247876337651483379731880898799076952340154521503375521103488550550468637297743386080284860162	617090134511253505989149294695806589697324626655310871313827657326800294523796027021756774551935818377248795949501424041701771296819850607128966959906659414732572568981750611191102991902321473874867601097111426800944188547793865
663396498468233344177673809473751774958817785254804128129611215907593651937470600766283056187138956934221840240015076040722622520521143958408561980587774330901905111963816840510334825493631817797198205988610429156196997124828340465430805719161456987390025407536556658117204332999685618964512370977159272769	814491558254739276323341408145087297780726682894998623119420314213083389265931040863187213970270263977688560319061173328621624777347417433682689662793512842326189515817189562084250277963857540739554357244272419335525591802990446
572328537863833089457809556432596370536501825279362811557668673635732135199195517536332632774017930152308639669050107073295541602122471742629479078087577446957900663131611225984832725336013776981321301965630287769161275623406602840483582387978207194481458633445293049906120127833356149179412387345022040492	756523983667294641479018000864874894169557884391092254052233209379359633920478613172517564447046787538552723128774646996279078001198272404524433284437399374640680600104132384683396080133542236040533898872940034522645509357872637
668590590315182521229284152414027866602484738298406330261097147067195648280777237853103935027506674070054579198956748456413478883459071001209427504232863820	817673889955636605460959528522429217273716321560479016735529190762369992107091459427828287607648228237856829847268406013680991488884386215563771055139246
678693431384719987293838095043719676411830623817886365185801096517879764208168124924944670140509448859500560552934097660569666645024598176182648073007806727	823828520618653980874020571048236267594978617240906059399936796647460348177878643131017454508662921015746900770981454765677386321602216291972295608776185
126060216042623682591163276977820029584032289865257924658324539922919028337839162119190929541406317386530968873365643443865283740419740963423036828589351362	355049596595494926625052503005303187483173561865354497546721907423325580470862405934691428410200149861562620322363765917962252638258938516314402484706924
282317724487772564079827738168821264927333038510015487408649117088717237247128064498716120939073008885849472998886662072137616336692605188206153673062650698	531335792590497863290131988340256454657803065106676050549959926662130745364900199163029619843768620703947886970960606846800050585134059901559824803700091
992432895521167758152510762542413658789193068264498920965063221208610892040068222171524067893687438965120174523303887304905505152225304297512017376283860354	996209262916766779323544090313401377813283232927662254537718622610449430320720479545208558561797718024242116231609697865348370731883628163262551648225592
931458621026537433439003373895150693814289638950912271735293706515881567661331420074125823642869762562359666389066047624560644536008136336812294738408389863	965121039573035851159511033714521174629509451794033496378388133451879671216801160287698321280688623406463259946161602569208648971584392481244655406722871
168408371004373239711919285890329468661051244615189825012111751895495159735353679438060390541030665271820180664610308440780028171608807211033249941574080002	410375889891661690578584059363281559614780160832006447221757888174006473420220599710101803885226872657525207857809791958713072627530919142644288333033434
586098557282222659564301459015746337268082195473546235713216550736774270904575551055167736679025922963966411899655520739970140883077755389413895790826727312	765570739567691849989859279660136962110380706907406415626725626669689147788710916599268399402287342812974117110692308997480686396074867946175437687684778
52124949573480035210552103146500005092215954883781010021252344720984587573589375050940698936430799944074038929052291583104965161563987460590653194488429485	228308890701785932904427434963138052859607266340548974017014250566778477247302201124562452404606760065994823865185245365599421037685650334536776019788334
706701657657212416918365140630107493259858579420234188409836152114597648797392885933556458270791423085294556112795575423526381224506279357337693693416525712	840655492849010305518557560171981273006194367496121417187124199632634594538500083385999987688460238821915114113158536835590803329169562368818175264359013
8821733336248402870150862847895172858412125297839751390815661609643869412230314278138172234836555073680854185737155437597138319104943053642460514689885656	93924082834214584999813407926011262572391701719959978724267669883531034200308434204089254387305696685762308049461892782215080903361321253943511944262702
858101436317411672308822673160034575835119178238865379863030192274959467074027626337920919480435312214723671831420713328364851523005287999224238560268659467	926337647036657833959046077919720768936846186473207899941741695909615069455161730176733623489757284114843343992016296458277372226275600928668249877560245
978578071587327897732144141300455759579479646064363132517652419502141167862991988707522692996100175532079342625687719858870033484436173501522307453319711919	989231050658706273573929056540837396202455703861812416545350162895319414277748081636156266051332074077429355483593556672166895540496317663333446872845069
886863305796204801994023649767482262642219359888057410701211920161394510379810253622219170857941254950680899951103305233729627426354186447751791710843292052	941734201245874260721242244488827296946163477418348360275769032850257402385596621622082006303749047660622488879572924638907297469868140607365207780141240
767216723311738957604841442668267087426418632970898813014304706450670229612348446486097133306081322936371664444923594555941089788441164185450569207422836280	875909083930369429528597642859983261430699227696040270932232835009052175241523989766659437484578043718762115730857417254726690062320847042980881067243818
105675904795898582667553668696108765166735918083534429734864712092722315615975721312621862367795368008961363622595732750856584141050188131398552280500695604	325078305637116582205687533307785896020180658633806843628648160332608952332622285670907543135803327357499490306026641807968697362530675486281957501962704
61741673192436400594242846915062661306040220915104059640544194877430194745882310408337442887954545776142691033529693152291464527230912818784798353974798058	248478717785721843084218823086165714784017627364970308973401788941962695245438441381265205699356247259696597460652249632791716879385078716468359021707794
524552344812284458593899235011867613564034458848954477667117873934584115089336984393931251364959858182480309140009399487064989090322868714733242101067076841	724259860003496575520481701810381415918947923008455894345745092883184899329965068995505264815359965407813370217436862387039210454912345519984588210161899
427860884471069634467380214913266571694074100969815203697011475768954754475503657094646312622052202069587526013145655417348022487919730340758219560445036715	654110758565450927920409973617353268055380067620543531562387259171145017839073841434053925504455195508819485447386137978641547781417290166560936143565548
362821864788702463630998755671415275017007319024417962624522095814839313981989536475119906200858699923406332214074013742991447854335196829753272959291963136	602346963791386985049599557427767890642088312826177185946650395317206920802453397591787245679092229324962679701229750383791437474574719435876005831104090
907872191770046945489973942221985045103479528245818297021046892469079115985569195905315320230645772496684593113473838671379496356475652235914587360873103195	952823274154261486619698867666337835657234160007440974641631775993479394401354877246868672771951723007747877529374592322436417438624867966724349707389639
696779947908499202754195178148345860985336550880243715156412096755107215700962848573232442734927898539379453518588938086594951857729335026087907773055352357	834733459200300178523259013528949981632178935271905467443682264814188414134687037983860138759766625505792123234735935264214757073122397039863484909894738
0	0
1	1000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512462418027925368606322060748549967915706611332963752796377899975250576391030285735054779985802985137267298431

# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
## category: half-ULP-tie
188776061678810495660972352901383589050142417002469277722879775738063167064379558924093885795442448886275616257426553151140655195759419222917254289396786374	434483672511189418643628259485172268897976788710214775342755600290534873633695163052589569912584855720317688549491261536777956808194097878308938887013310
573204291125013878637773551811589428305591439317536448412032766546156398308550131452607968511881472304133804942973178490175208576903771329158317054505569728	757102563147829977439872865403122474940801329186769292143331443384418188450192995195812737431575526492422148490060095723742085098450475239592383089226550
690412921417384876960334591222841186862304051566607542610666542747679294218241604085348036842830045151651763976788672517961813159872282631216747771242956068	830910898603084202535410743809421585075044035315404771667146767218509567228719982340478265846607861011709120864486994699005312595841738719631952405121448
187267496890135149412566152450900776129665913388311381755507234124687982929105405130737143063759051819035102691529715471698552952475888230221624708805908054	432744147147174192041592083795191514716926723247449896447555308414293257209067515363715516989875163899842751664542705196377449955190324454982220554826649
987202805653774465933316929547171218097769221464692757208588574394880918442408381157410167311536344250682960740160604054692271048071198482828955041951226251	993580799761033257625455235037789160944502392684992381193581201643375222475825330430772029172966734745248838349904245019751421747251937400361621491933332
924048476350946243523399975208296674158170290702866072534738782334568674194589304311766628653658479123137452486100076490283688077352204436422914125857787876	961274402213512727803716284891830934799553196818880714938644601807165160121007871390271076437259070442227766512445016517430854946364408517044614083686313
769566118783960379368603813343679771950955439059800188771086151508024337464318448892838915692937966284984860371458966969656446948245292168799442749506121492	877249177134957693069679696276870887750725020313791413495468304176543676708322088584215378599610570065449058733271478561405105273215446311871088794515898
890080007993338651164435061387218843329933815828589975107426182515343896157829173975631887553066746169055711798422351389248374085511992422024768998001887690	943440516404366985549792946556363700666601267387942714420321452635750531975846221368395224201955921871030070775728939277243030135556549009928571039029221
735836945389878265044965514591244852746456748086094557851474393524267864268542392973686358492870196149064048825639469327451445519002277701926233966214898822	857809387562224260043489939105664656874587586113546634026689556201534107425953376734307088954730514380170232568354925163839709294445115238184696991477105
556768175554203837233427641750255109264839025777259127903610930673902505509110257269407628108869889967326094615630979675046355798878998038573490272081534584	746168999325356478745621810192964645359215859862223180874774803083311146234335634069722965083836195542637636830888436362410425666568781165878147383954513
189392978409606665239050981982040050821686325257987230028308800984658203308386826300467319093539981645149936924516071248352282230552885593004022191359917408	435193035800903718045032839741659226298592187877843155902614606892312891841917608576872303157718925598331453151294764692877709304598584612046515405128328
591593218488165434894209803586440350045969262369885924973472629562827010945675019119704063077682538970679868993150337349270868175680368692153219676317396718	769150972493804648439270757865081760518460739308826505554362468245367955035765483960747887374594059946033690349438691565189569554303949365291173530605442
276456607988433237464071496484892004157856171220620711753016004605487006302611429793065357533237254067895334355839421169298733413137611163941660994722128384	525791411101810636512761608022690139604226183784633627931355924726816982150145945304664478128110834802108987834551646610211911840687723673244839787188995
753320372884668632006989854662327998006893740368328139386996860169764153725475808562669801037039684380930913002783736771685810089406726500161028082646263419	867940304908505001964748324481173443168691013941441802128674952651184940978298551865585093321008806666671695530946050486402400354359301534258902302859974
969588023326458611093305417693002023240206512576569126085560701746285189887923077848760009823125026878636959525347364180839559740185740962657480382758184261	984676608499693472378909122696916147778968220478203455472934530075317591455173634697913415316738839786362001218634504301358870843003398916367892624245256
616789945007202857355743205894353981136563192623133900949029112521243031497618746285730608865660693219399513410828400481130005663203239509345541525020815732	785359755148685255926843297798168363695438844184071771035668319212919223100573724231533976718471489796991212377007823026487901395345943681419172150925428
153749559751139562466931401938569159721145602911940686445083935938703059285600257913783481514472399749981627897226965795491430178844679856510415351384086697	392109117148708444140584979792570949723584377894827396084518150862344043430318591977476380453986868863795670348435764323994771075506421051766548994507805
977275001277330873454632505118011502243790520704472994695438818449676802807714022574351718908991596813838351139187565086491267067301381386631526528642850949	988572203370765869246864295717825595653058924153624477810865061737573858551620737270649552385437457842869645595309004541760092850924159455479729946985540
883048885050393313032754538786933846312067948516638837617688217500882818836698077784631743898385095183640879295017390294027886563639789896953258345916163118	939706808025989196106834580085671966642709408756880745548349486923111441099640080547449125726784673036397485223530292062856385401952648898912576969122815
436775686607713464028259290597245375104300151880468933926766812238811459519062564956393759930706369556030152417384438410890702411297367404519825835023493832	660890071500331637436513661269199500867060088960717119136769300676960028056831208255063832889311799783060872716829067091800896473262969721519232955362052
774997745803421573232439092092002561992447236572858785114065523024344318217533280485636583324792616553882397186397679650239881935354670084770052822764045786	880339562784396037751375047286552580061921538692928081935165904199627007235938487287888694181283211588165585370575239043982131132355166876828007717161710
369070835745729765347266672525307152484752668393717010308214342158939256787108708885842546354483832230861866453336289820928647462866725333818290983792765571	607512004610386086276161465120430381496393835192524863894883813376581575066689818613000035007927848035031693641382330544984064161642143310389806832958033
249575354216856861126266304079428188610624954963523266379928821743006015307201703768626292155854971392681234961627484393610312109514487884204564767950945645	499575173739505255177480848957557307043334299333205196708625930021909107625146672570961610146937220663882880060643098992382628603170915146984070180609120
28825267462554403917756129477371892022273316951611129177748957747935680463226703332559225643489258116804434034445106754772583879830015264056707423070041994	169780056138977654414371676997359951230937660377336860256296002906589579947115534476483713584621245046242826584010151438389250072878982996833319643003657
615597070100752085294373674811710570647246834190199902831639357694826106855883889340724569681940577655501829025499055137090080476990917061012992998447253990	784599942710138161589411299157425719760817197693381512251046823874165180087038975900395053980467239889304899711638276418032887120932936698393605984778507
## category: catastrophic cancellation
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000005000000000000000000000000000000000
1000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000004999999999999999999999999999999999999999999987500000000000000000000000000000000000000000062500000000000000
999999999999999999999999999999999999999999999999999900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999998750000000000000000000000000000000000000000000
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999900000000000000	999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999950000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000500000000000000000000000000000000000000000000000000000000000000000000
999999999999999999999999999999999999999999999999999999999999999900000000000000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999998750000000000000000000
1000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000049999999999999999999999999999998750000000000000000000000000000062499999999999999999999999999996093750000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000004999999999999999999999999999999999999999999999999999999999999999999987500000000000
999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999999999987
999999999999999999999999999999999900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999949999999999999999999999999999999998749999999999999999999999999999999937499999999999999999999999999999996093750000000
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000004999999999999999999999999999999999999999999999999999999987500000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000500000000000000000000000000000000000000000000000000000
1001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000499875062460964823258287700109753027590031219780479551442971840836093890879944856933288426795151877873337158032830529173106942653255163851084326079
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999900000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999950000000000000000000000000000000000000000000000
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999990000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000050000000000000000000000000000000000000000000000
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999999999999999999999999999500000000000000000000000000000000000000000000000000000000000000
999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999875000000000000000000000000000000000000000
999999999999999999990000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999994999999999999999999987499999999999999999937499999999999999999609374999999999999997265624999999999999979492187499999999999838867187
999999999999999999999999999999999999999999999999999999999999999999999999999999999000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999999999999999999999999999999999999999999999500000000000000000000000000000000000000000000000000000000000000000000
999999999999999999999999999999999999999900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	999999999999999999999999999999999999999949999999999999999999999999999999999999998749999999999999999999999999999999999999937500000000000000000000000000
1000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000499999999999999999999999999999999999999999999999999999999999875000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000499999999999999999999999999999999999999999999999999999999999999999999999875000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000500000000000000000000
## category: asymptote stress
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005514854885603045388001469051959670
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951873472841528400551485488560304538800146905195967
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295187347284152840055148548856030453880014690519597
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005514854885603045388001469051960
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951873472841528400551485488560304538800146905196
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295187347284152840055148548856030453880014690520
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005514854885603045388001469052
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951873472841528400551485488560304538800146905
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295187347284152840055148548856030453880014691
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005514854885603045388001469
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	31622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951873472841528400551485488560304538800147
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	3162277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295187347284152840055148548856030453880015
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	316227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005514854885603045388001
## category: inverse-identity
250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
49000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## category: perfect-power ± ULP
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
15999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
24999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
48999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
49000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
120999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	11000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
121000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	11000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
121000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	11000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
255999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
256000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	16000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
528999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	23000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
## category: constant edges
1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497100
2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497100
2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497100
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	1732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575675626141415406703029969945094998952478811655512094
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575675626141415406703029969945094998952478811655512094
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	1732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248575675626141415406703029969945094998952478811655512095
4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782274969508176150773783504253267724447073863586360121533
5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782274969508176150773783504253267724447073863586360121533
5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	2236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782274969508176150773783504253267724447073863586360121534
3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408127	1772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665416226823624282570666236152865724422602525093709602
3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128	1772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665416226823624282570666236152865724422602525093709603
3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408129	1772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665416226823624282570666236152865724422602525093709603
2718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260	1648721270700128146848650787814163571653776100710148011575079311640661021194215608632776520056366643002866637756307797004671166975219609159840971452490
2718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295261	1648721270700128146848650787814163571653776100710148011575079311640661021194215608632776520056366643002866637756307797004671166975219609159840971452490
2718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295262	1648721270700128146848650787814163571653776100710148011575079311640661021194215608632776520056366643002866637756307797004671166975219609159840971452490
499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999	707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512462418027925368606322060748549
500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512462418027925368606322060748550
500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001	707106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512462418027925368606322060748551
2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000	1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497100
